{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6c3046ec",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\penri\\AppData\\Local\\Temp\\ipykernel_1900\\2979793285.py:9: DeprecationWarning: `set_matplotlib_formats` is deprecated since IPython 7.23, directly use `matplotlib_inline.backend_inline.set_matplotlib_formats()`\n",
      "  set_matplotlib_formats('retina')\n"
     ]
    },
    {
     "data": {
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       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ID</th>\n",
       "      <th>Day</th>\n",
       "      <th>Group</th>\n",
       "      <th>Originality</th>\n",
       "      <th>Interestingness</th>\n",
       "      <th>Writing</th>\n",
       "      <th>Coherence</th>\n",
       "      <th>Overall</th>\n",
       "      <th>Evaluator</th>\n",
       "      <th>unique_id</th>\n",
       "      <th>external</th>\n",
       "      <th>Humanlikeness</th>\n",
       "      <th>English</th>\n",
       "      <th>Experience</th>\n",
       "      <th>Ability</th>\n",
       "      <th>DAT</th>\n",
       "      <th>Total</th>\n",
       "      <th>Idea</th>\n",
       "      <th>Outline</th>\n",
       "      <th>Write</th>\n",
       "      <th>Edit</th>\n",
       "      <th>Satisfaction</th>\n",
       "      <th>Flexibility</th>\n",
       "      <th>Goal</th>\n",
       "      <th>Again</th>\n",
       "      <th>AI_Helpfulness</th>\n",
       "      <th>AI_Satisfaction</th>\n",
       "      <th>AI_Contribution</th>\n",
       "      <th>DAT_Group</th>\n",
       "      <th>Group_</th>\n",
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       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Human Creativity</td>\n",
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       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>4.0</td>\n",
       "      <td>Benjamin Joers</td>\n",
       "      <td>1_1</td>\n",
       "      <td>0</td>\n",
       "      <td>4.5</td>\n",
       "      <td>3.0</td>\n",
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       "      <td>86.81</td>\n",
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       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Human Creativity</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>Rio Dharma</td>\n",
       "      <td>1_1</td>\n",
       "      <td>0</td>\n",
       "      <td>4.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>86.81</td>\n",
       "      <td>80.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>55.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>Human Creativity</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>2.0</td>\n",
       "      <td>allison liegner</td>\n",
       "      <td>1_2</td>\n",
       "      <td>0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>86.81</td>\n",
       "      <td>85.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>70.0</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>Human Creativity</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>6</td>\n",
       "      <td>7.0</td>\n",
       "      <td>Ryan Ho</td>\n",
       "      <td>1_2</td>\n",
       "      <td>0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>86.81</td>\n",
       "      <td>85.0</td>\n",
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       "      <td>70.0</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>Human Confirmation</td>\n",
       "      <td>6</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>6.0</td>\n",
       "      <td>Nathan Kidambi</td>\n",
       "      <td>2_1</td>\n",
       "      <td>0</td>\n",
       "      <td>6.5</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
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       "      <td>5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>Pema Euden</td>\n",
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       "      <td>3.0</td>\n",
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       "      <td>2.0</td>\n",
       "      <td>87.08</td>\n",
       "      <td>45.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>25.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>5.0</td>\n",
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       "    <tr>\n",
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       "      <td>295</td>\n",
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       "      <td>Human Creativity</td>\n",
       "      <td>5</td>\n",
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       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4.0</td>\n",
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       "      <td>0.0</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2</td>\n",
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       "    <tr>\n",
       "      <th>2193</th>\n",
       "      <td>295</td>\n",
       "      <td>1</td>\n",
       "      <td>Human Creativity</td>\n",
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       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>Alan Wu</td>\n",
       "      <td>295_1</td>\n",
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       "      <td>1.0</td>\n",
       "      <td>74.63</td>\n",
       "      <td>66.0</td>\n",
       "      <td>1.0</td>\n",
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       "      <td>5.0</td>\n",
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       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>2194</th>\n",
       "      <td>295</td>\n",
       "      <td>2</td>\n",
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       "      <td>5</td>\n",
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       "      <td>6</td>\n",
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       "      <td>55.0</td>\n",
       "      <td>5.0</td>\n",
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       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
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       "      <td>5.0</td>\n",
       "      <td>71.0</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>2195</th>\n",
       "      <td>295</td>\n",
       "      <td>2</td>\n",
       "      <td>Human Creativity</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>6.0</td>\n",
       "      <td>Ziqi Yang</td>\n",
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       "      <td>71.0</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2196 rows × 30 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       ID  Day               Group  Originality  Interestingness  Writing  \\\n",
       "0       1    1    Human Creativity            5                3        4   \n",
       "1       1    1    Human Creativity            5                6        4   \n",
       "2       1    2    Human Creativity            2                1        3   \n",
       "3       1    2    Human Creativity            6                7        7   \n",
       "4       2    1  Human Confirmation            6                5        6   \n",
       "...   ...  ...                 ...          ...              ...      ...   \n",
       "2191  294    2             Copilot            6                4        5   \n",
       "2192  295    1    Human Creativity            5                4        4   \n",
       "2193  295    1    Human Creativity            5                5        6   \n",
       "2194  295    2    Human Creativity            5                5        5   \n",
       "2195  295    2    Human Creativity            5                5        7   \n",
       "\n",
       "      Coherence  Overall        Evaluator unique_id  external  Humanlikeness  \\\n",
       "0             7      4.0   Benjamin Joers       1_1         0            4.5   \n",
       "1             5      5.0       Rio Dharma       1_1         0            4.5   \n",
       "2             5      2.0  allison liegner       1_2         0            3.0   \n",
       "3             6      7.0          Ryan Ho       1_2         0            3.0   \n",
       "4             6      6.0   Nathan Kidambi       2_1         0            6.5   \n",
       "...         ...      ...              ...       ...       ...            ...   \n",
       "2191          5      5.0       Pema Euden     294_2         1            3.0   \n",
       "2192          4      4.0       Pema Euden     295_1         1            6.5   \n",
       "2193          5      5.0          Alan Wu     295_1         1            6.5   \n",
       "2194          6      5.0       Pema Euden     295_2         1            3.5   \n",
       "2195          7      6.0        Ziqi Yang     295_2         1            3.5   \n",
       "\n",
       "      English  Experience  Ability    DAT  Total  Idea  Outline  Write  Edit  \\\n",
       "0         3.0         1.0      2.0  86.81   80.0  12.0      8.0   55.0   5.0   \n",
       "1         3.0         1.0      2.0  86.81   80.0  12.0      8.0   55.0   5.0   \n",
       "2         3.0         1.0      2.0  86.81   85.0  10.0     20.0   15.0  40.0   \n",
       "3         3.0         1.0      2.0  86.81   85.0  10.0     20.0   15.0  40.0   \n",
       "4         2.0         1.0      1.0  89.58    NaN  45.0      NaN    NaN   NaN   \n",
       "...       ...         ...      ...    ...    ...   ...      ...    ...   ...   \n",
       "2191      3.0         3.0      2.0  87.08   45.0   3.0      5.0   25.0  12.0   \n",
       "2192      2.0         1.0      1.0  74.63   66.0   1.0      5.0   40.0  20.0   \n",
       "2193      2.0         1.0      1.0  74.63   66.0   1.0      5.0   40.0  20.0   \n",
       "2194      2.0         1.0      1.0  74.63   55.0   5.0     20.0   25.0   5.0   \n",
       "2195      2.0         1.0      1.0  74.63   55.0   5.0     20.0   25.0   5.0   \n",
       "\n",
       "      Satisfaction  Flexibility  Goal  Again  AI_Helpfulness  AI_Satisfaction  \\\n",
       "0              1.0          4.0   2.0    0.0             NaN              NaN   \n",
       "1              1.0          4.0   2.0    0.0             NaN              NaN   \n",
       "2              3.0          3.0   3.0    0.0             4.0              5.0   \n",
       "3              3.0          3.0   3.0    0.0             4.0              5.0   \n",
       "4              2.0          6.0   2.0    0.0             NaN              NaN   \n",
       "...            ...          ...   ...    ...             ...              ...   \n",
       "2191           7.0          6.0   5.0    1.0             7.0              7.0   \n",
       "2192           5.0          4.0   2.0    0.0             NaN              NaN   \n",
       "2193           5.0          4.0   2.0    0.0             NaN              NaN   \n",
       "2194           3.0          4.0   5.0    1.0             6.0              5.0   \n",
       "2195           3.0          4.0   5.0    1.0             6.0              5.0   \n",
       "\n",
       "      AI_Contribution  DAT_Group  Group_  \n",
       "0                 NaN          3       1  \n",
       "1                 NaN          3       1  \n",
       "2                70.0          3       1  \n",
       "3                70.0          3       1  \n",
       "4                 NaN          3       2  \n",
       "...               ...        ...     ...  \n",
       "2191             91.0          3       3  \n",
       "2192              NaN          2       1  \n",
       "2193              NaN          2       1  \n",
       "2194             71.0          2       1  \n",
       "2195             71.0          2       1  \n",
       "\n",
       "[2196 rows x 30 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "import matplotlib.transforms as transforms\n",
    "import seaborn as sns\n",
    "from IPython.display import set_matplotlib_formats\n",
    "%matplotlib inline\n",
    "set_matplotlib_formats('retina')\n",
    "from scipy import stats\n",
    "import statsmodels.formula.api as smf\n",
    "import statsmodels.api as sm\n",
    "import warnings\n",
    "import matplotlib.path as mpath\n",
    "sns.set(rc={\"figure.dpi\":100, 'savefig.dpi':300})\n",
    "sns.set_context('notebook')\n",
    "sns.set_style(\"ticks\")\n",
    "warnings.filterwarnings('ignore')\n",
    "pd.set_option('display.max_columns', None)\n",
    "df = pd.read_csv('Replication Data for Designing Human and Generative AI Collaboration.csv').iloc[:,1:]\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c913bca",
   "metadata": {},
   "source": [
    "# Table S.3: Difference-in-Differences Results for Total Completion Time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0306270a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  Total   R-squared:                       0.248\n",
      "Model:                            OLS   Adj. R-squared:                  0.234\n",
      "Method:                 Least Squares   F-statistic:                     18.00\n",
      "Date:                Sat, 09 Nov 2024   Prob (F-statistic):           6.49e-26\n",
      "Time:                        16:34:38   Log-Likelihood:                -2280.2\n",
      "No. Observations:                 502   AIC:                             4580.\n",
      "Df Residuals:                     492   BIC:                             4623.\n",
      "Df Model:                           9                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===============================================================================================================================================\n",
      "                                                                                  coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-----------------------------------------------------------------------------------------------------------------------------------------------\n",
      "Intercept                                                                      54.7543     12.882      4.251      0.000      29.445      80.064\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Copilot]                 -3.9105      3.586     -1.091      0.276     -10.955       3.135\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Human Creativity]        -1.3765      3.545     -0.388      0.698      -8.342       5.589\n",
      "Day                                                                           -26.4200      3.678     -7.183      0.000     -33.647     -19.193\n",
      "Day:C(Group, Treatment(reference=\"Human Confirmation\"))[T.Copilot]              3.2993      5.115      0.645      0.519      -6.752      13.350\n",
      "Day:C(Group, Treatment(reference=\"Human Confirmation\"))[T.Human Creativity]     0.1834      5.031      0.036      0.971      -9.702      10.069\n",
      "DAT                                                                             0.3245      0.147      2.209      0.028       0.036       0.613\n",
      "Ability                                                                         0.5364      1.778      0.302      0.763      -2.956       4.029\n",
      "Experience                                                                     -2.5071      1.690     -1.483      0.139      -5.828       0.814\n",
      "English                                                                        -2.3031      2.486     -0.926      0.355      -7.187       2.581\n",
      "==============================================================================\n",
      "Omnibus:                      561.396   Durbin-Watson:                   1.946\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            52336.713\n",
      "Skew:                           4.988   Prob(JB):                         0.00\n",
      "Kurtosis:                      52.017   Cond. No.                     1.05e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.05e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "tmp = df.groupby(by=['ID', 'Day'])[['Group', 'Total', 'DAT', 'Ability', 'Experience', 'English']].first().reset_index()\n",
    "tmp['Day'] = tmp['Day'] - 1\n",
    "model = smf.ols('Total ~ Day*C(Group, Treatment(reference=\"Human Confirmation\")) + DAT + Ability + Experience + English', \n",
    "                data=tmp).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3ae1b5d",
   "metadata": {},
   "source": [
    "# Table S.4: Differences in Additional Quality Metrics Among Groups on Day 2 (Writing with AI Assistance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "4f45447c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:            Originality   R-squared:                       0.014\n",
      "Model:                            OLS   Adj. R-squared:                  0.008\n",
      "Method:                 Least Squares   F-statistic:                     2.459\n",
      "Date:                Fri, 08 Nov 2024   Prob (F-statistic):             0.0229\n",
      "Time:                        00:11:16   Log-Likelihood:                -1827.5\n",
      "No. Observations:                1068   AIC:                             3669.\n",
      "Df Residuals:                    1061   BIC:                             3704.\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===========================================================================================================================================\n",
      "                                                                              coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------------------------------------------------------------\n",
      "Intercept                                                                   3.6671      0.514      7.141      0.000       2.659       4.675\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Copilot]              0.0535      0.102      0.524      0.600      -0.147       0.254\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Human Creativity]    -0.0409      0.103     -0.399      0.690      -0.242       0.161\n",
      "DAT                                                                         0.0208      0.006      3.508      0.000       0.009       0.032\n",
      "English                                                                    -0.0846      0.098     -0.860      0.390      -0.278       0.108\n",
      "Experience                                                                  0.0117      0.069      0.171      0.864      -0.123       0.146\n",
      "Ability                                                                    -0.0693      0.072     -0.959      0.338      -0.211       0.072\n",
      "==============================================================================\n",
      "Omnibus:                       74.615   Durbin-Watson:                   1.836\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               89.589\n",
      "Skew:                          -0.709   Prob(JB):                     3.52e-20\n",
      "Kurtosis:                       3.050   Cond. No.                     1.03e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.03e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Originality ~ C(Group, Treatment(reference=\"Human Confirmation\")) + DAT + English + Experience + Ability',\n",
    "                data=df[df.Day==2]).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "8dd37091",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:        Interestingness   R-squared:                       0.012\n",
      "Model:                            OLS   Adj. R-squared:                  0.007\n",
      "Method:                 Least Squares   F-statistic:                     2.186\n",
      "Date:                Fri, 08 Nov 2024   Prob (F-statistic):             0.0421\n",
      "Time:                        00:12:15   Log-Likelihood:                -1919.1\n",
      "No. Observations:                1068   AIC:                             3852.\n",
      "Df Residuals:                    1061   BIC:                             3887.\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===========================================================================================================================================\n",
      "                                                                              coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------------------------------------------------------------\n",
      "Intercept                                                                   5.3118      0.558      9.511      0.000       4.216       6.408\n",
      "C(Group, Treatment(reference=\"Human Creativity\"))[T.Copilot]               -0.0417      0.110     -0.380      0.704      -0.257       0.174\n",
      "C(Group, Treatment(reference=\"Human Creativity\"))[T.Human Confirmation]    -0.3031      0.112     -2.709      0.007      -0.523      -0.084\n",
      "DAT                                                                         0.0021      0.006      0.333      0.739      -0.011       0.015\n",
      "English                                                                    -0.0957      0.107     -0.892      0.372      -0.306       0.115\n",
      "Experience                                                                 -0.1146      0.075     -1.535      0.125      -0.261       0.032\n",
      "Ability                                                                    -0.0335      0.079     -0.425      0.671      -0.188       0.121\n",
      "==============================================================================\n",
      "Omnibus:                       48.205   Durbin-Watson:                   1.992\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               53.889\n",
      "Skew:                          -0.545   Prob(JB):                     1.99e-12\n",
      "Kurtosis:                       2.850   Cond. No.                     1.03e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.03e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Interestingness ~ C(Group, Treatment(reference=\"Human Creativity\")) + DAT + English + Experience + Ability',\n",
    "                data=df[df.Day==2]).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "adc01416",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Writing   R-squared:                       0.012\n",
      "Model:                            OLS   Adj. R-squared:                  0.007\n",
      "Method:                 Least Squares   F-statistic:                     2.195\n",
      "Date:                Fri, 08 Nov 2024   Prob (F-statistic):             0.0413\n",
      "Time:                        00:12:49   Log-Likelihood:                -1771.7\n",
      "No. Observations:                1068   AIC:                             3557.\n",
      "Df Residuals:                    1061   BIC:                             3592.\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===========================================================================================================================================\n",
      "                                                                              coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------------------------------------------------------------\n",
      "Intercept                                                                   6.3403      0.486     13.033      0.000       5.386       7.295\n",
      "C(Group, Treatment(reference=\"Human Creativity\"))[T.Copilot]               -0.0992      0.096     -1.037      0.300      -0.287       0.089\n",
      "C(Group, Treatment(reference=\"Human Creativity\"))[T.Human Confirmation]    -0.2850      0.097     -2.924      0.004      -0.476      -0.094\n",
      "DAT                                                                        -0.0092      0.006     -1.638      0.102      -0.020       0.002\n",
      "English                                                                     0.0314      0.093      0.336      0.737      -0.152       0.215\n",
      "Experience                                                                 -0.0440      0.065     -0.676      0.499      -0.172       0.084\n",
      "Ability                                                                    -0.0085      0.069     -0.124      0.901      -0.143       0.126\n",
      "==============================================================================\n",
      "Omnibus:                      117.487   Durbin-Watson:                   2.043\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              156.086\n",
      "Skew:                          -0.880   Prob(JB):                     1.28e-34\n",
      "Kurtosis:                       3.639   Cond. No.                     1.03e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.03e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Writing ~ C(Group, Treatment(reference=\"Human Creativity\")) + DAT + English + Experience + Ability',\n",
    "                data=df[df.Day==2]).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "2fdbcdea",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:              Coherence   R-squared:                       0.022\n",
      "Model:                            OLS   Adj. R-squared:                  0.017\n",
      "Method:                 Least Squares   F-statistic:                     4.021\n",
      "Date:                Fri, 08 Nov 2024   Prob (F-statistic):           0.000544\n",
      "Time:                        00:13:58   Log-Likelihood:                -1815.6\n",
      "No. Observations:                1068   AIC:                             3645.\n",
      "Df Residuals:                    1061   BIC:                             3680.\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===========================================================================================================================================\n",
      "                                                                              coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------------------------------------------------------------\n",
      "Intercept                                                                   6.1199      0.507     12.073      0.000       5.125       7.115\n",
      "C(Group, Treatment(reference=\"Human Creativity\"))[T.Copilot]               -0.2314      0.100     -2.320      0.021      -0.427      -0.036\n",
      "C(Group, Treatment(reference=\"Human Creativity\"))[T.Human Confirmation]    -0.4599      0.102     -4.529      0.000      -0.659      -0.261\n",
      "DAT                                                                        -0.0078      0.006     -1.338      0.181      -0.019       0.004\n",
      "English                                                                     0.0122      0.097      0.125      0.901      -0.179       0.203\n",
      "Experience                                                                 -0.0235      0.068     -0.347      0.729      -0.157       0.109\n",
      "Ability                                                                     0.0124      0.071      0.174      0.862      -0.128       0.153\n",
      "==============================================================================\n",
      "Omnibus:                       65.389   Durbin-Watson:                   2.125\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               76.632\n",
      "Skew:                          -0.656   Prob(JB):                     2.29e-17\n",
      "Kurtosis:                       3.048   Cond. No.                     1.03e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.03e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Coherence ~ C(Group, Treatment(reference=\"Human Creativity\")) + DAT + English + Experience + Ability',\n",
    "                data=df[df.Day==2]).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcc44adf",
   "metadata": {},
   "source": [
    "# Table S.5: Influence of Additional Quality Metrics on Overall Quality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "976edcb5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Overall   R-squared:                       0.799\n",
      "Model:                            OLS   Adj. R-squared:                  0.799\n",
      "Method:                 Least Squares   F-statistic:                     2176.\n",
      "Date:                Fri, 08 Nov 2024   Prob (F-statistic):               0.00\n",
      "Time:                        00:47:48   Log-Likelihood:                -2017.0\n",
      "No. Observations:                2196   AIC:                             4044.\n",
      "Df Residuals:                    2191   BIC:                             4073.\n",
      "Df Model:                           4                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===================================================================================\n",
      "                      coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-----------------------------------------------------------------------------------\n",
      "Intercept          -0.5600      0.064     -8.712      0.000      -0.686      -0.434\n",
      "Originality         0.2027      0.012     17.060      0.000       0.179       0.226\n",
      "Interestingness     0.4231      0.012     34.316      0.000       0.399       0.447\n",
      "Writing             0.1671      0.012     13.763      0.000       0.143       0.191\n",
      "Coherence           0.2944      0.012     23.871      0.000       0.270       0.319\n",
      "==============================================================================\n",
      "Omnibus:                      361.256   Durbin-Watson:                   1.970\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1213.182\n",
      "Skew:                          -0.809   Prob(JB):                    3.64e-264\n",
      "Kurtosis:                       6.262   Cond. No.                         51.9\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Overall ~ Originality + Interestingness + Writing + Coherence',\n",
    "                data=df).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6be9381e",
   "metadata": {},
   "source": [
    "# Table S.6: Inequality in Completion Time on Day 2 (Writing with AI)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "84799b97",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>ID</th>\n",
       "      <th>Total_x</th>\n",
       "      <th>Group</th>\n",
       "      <th>English</th>\n",
       "      <th>Experience</th>\n",
       "      <th>Ability</th>\n",
       "      <th>DAT</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>80.0</td>\n",
       "      <td>Human Creativity</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>86.81</td>\n",
       "      <td>85.0</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
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       "      <td>2.0</td>\n",
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       "      <td>89.58</td>\n",
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       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>63.0</td>\n",
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       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>52.20</td>\n",
       "      <td>40.0</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5</td>\n",
       "      <td>67.0</td>\n",
       "      <td>Human Confirmation</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>74.41</td>\n",
       "      <td>55.0</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>7</td>\n",
       "      <td>65.0</td>\n",
       "      <td>Human Creativity</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>91.64</td>\n",
       "      <td>41.0</td>\n",
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       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>90.71</td>\n",
       "      <td>47.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>274</th>\n",
       "      <td>292</td>\n",
       "      <td>77.0</td>\n",
       "      <td>Human Creativity</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>75.07</td>\n",
       "      <td>60.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>275</th>\n",
       "      <td>293</td>\n",
       "      <td>70.0</td>\n",
       "      <td>Human Confirmation</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>80.36</td>\n",
       "      <td>59.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>276</th>\n",
       "      <td>294</td>\n",
       "      <td>67.0</td>\n",
       "      <td>Copilot</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>87.08</td>\n",
       "      <td>45.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>277</th>\n",
       "      <td>295</td>\n",
       "      <td>66.0</td>\n",
       "      <td>Human Creativity</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>74.63</td>\n",
       "      <td>55.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>278 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      ID  Total_x               Group  English  Experience  Ability    DAT  \\\n",
       "0      1     80.0    Human Creativity      3.0         1.0      2.0  86.81   \n",
       "1      2      NaN  Human Confirmation      2.0         1.0      1.0  89.58   \n",
       "2      4     63.0    Human Creativity      3.0         1.0      2.0  52.20   \n",
       "3      5     67.0  Human Confirmation      2.0         2.0      1.0  74.41   \n",
       "4      7     65.0    Human Creativity      3.0         1.0      1.0  91.64   \n",
       "..   ...      ...                 ...      ...         ...      ...    ...   \n",
       "273  291     47.0             Copilot      3.0         2.0      3.0  90.71   \n",
       "274  292     77.0    Human Creativity      3.0         1.0      2.0  75.07   \n",
       "275  293     70.0  Human Confirmation      3.0         1.0      1.0  80.36   \n",
       "276  294     67.0             Copilot      3.0         3.0      2.0  87.08   \n",
       "277  295     66.0    Human Creativity      2.0         1.0      1.0  74.63   \n",
       "\n",
       "     Total_y  \n",
       "0       85.0  \n",
       "1       90.0  \n",
       "2       40.0  \n",
       "3       55.0  \n",
       "4       41.0  \n",
       "..       ...  \n",
       "273     47.0  \n",
       "274     60.0  \n",
       "275     59.0  \n",
       "276     45.0  \n",
       "277     55.0  \n",
       "\n",
       "[278 rows x 8 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t1 = df[df.Day == 1]\n",
    "t2 = df[df.Day == 2]\n",
    "\n",
    "t1_ = t1.groupby(by='ID')['Total'].mean().reset_index()\n",
    "t1_ = pd.merge(t1_, t1[['ID', 'Group', 'English', 'Experience', 'Ability', 'DAT']], on=['ID']).drop_duplicates(keep='first').reset_index(drop=True)\n",
    "t2_ = t2.groupby(by='ID')['Total'].mean().reset_index()\n",
    "t2_ = pd.merge(t2_, t2[['ID', 'Group']], on=['ID']).drop_duplicates(keep='first').reset_index(drop=True)\n",
    "tt_ = pd.merge(t1_, t2_, on=['ID', 'Group'], how='left')\n",
    "\n",
    "tt_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "cbd3cb06",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Total_y   R-squared:                       0.091\n",
      "Model:                            OLS   Adj. R-squared:                  0.078\n",
      "Method:                 Least Squares   F-statistic:                     6.633\n",
      "Date:                Fri, 08 Nov 2024   Prob (F-statistic):             0.0123\n",
      "Time:                        23:12:07   Log-Likelihood:                -293.10\n",
      "No. Observations:                  68   AIC:                             590.2\n",
      "Df Residuals:                      66   BIC:                             594.6\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     21.2859      8.737      2.436      0.018       3.841      38.731\n",
      "Total_x        0.3176      0.123      2.575      0.012       0.071       0.564\n",
      "==============================================================================\n",
      "Omnibus:                        3.520   Durbin-Watson:                   1.645\n",
      "Prob(Omnibus):                  0.172   Jarque-Bera (JB):                3.068\n",
      "Skew:                           0.424   Prob(JB):                        0.216\n",
      "Kurtosis:                       2.398   Cond. No.                         279.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Total_y ~ Total_x',\n",
    "                data=tt_[tt_.Group=='Human Confirmation']).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "59d9eb06",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Total_y   R-squared:                       0.113\n",
      "Model:                            OLS   Adj. R-squared:                  0.041\n",
      "Method:                 Least Squares   F-statistic:                     1.559\n",
      "Date:                Fri, 08 Nov 2024   Prob (F-statistic):              0.185\n",
      "Time:                        23:10:36   Log-Likelihood:                -287.71\n",
      "No. Observations:                  67   AIC:                             587.4\n",
      "Df Residuals:                      61   BIC:                             600.7\n",
      "Df Model:                           5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     21.6476     30.632      0.707      0.482     -39.606      82.901\n",
      "Total_x        0.3222      0.135      2.389      0.020       0.053       0.592\n",
      "DAT            0.1489      0.371      0.401      0.690      -0.593       0.891\n",
      "Experience     1.9699      4.641      0.424      0.673      -7.310      11.249\n",
      "Ability        0.5075      4.047      0.125      0.901      -7.584       8.599\n",
      "English       -6.1062      5.189     -1.177      0.244     -16.482       4.270\n",
      "==============================================================================\n",
      "Omnibus:                        3.529   Durbin-Watson:                   1.596\n",
      "Prob(Omnibus):                  0.171   Jarque-Bera (JB):                3.062\n",
      "Skew:                           0.426   Prob(JB):                        0.216\n",
      "Kurtosis:                       2.391   Cond. No.                     1.46e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.46e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Total_y ~ Total_x + DAT + Experience + Ability + English',\n",
    "                data=tt_[tt_.Group=='Human Confirmation']).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "364badfe",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Total_y   R-squared:                       0.003\n",
      "Model:                            OLS   Adj. R-squared:                 -0.009\n",
      "Method:                 Least Squares   F-statistic:                    0.2499\n",
      "Date:                Fri, 08 Nov 2024   Prob (F-statistic):              0.618\n",
      "Time:                        23:12:27   Log-Likelihood:                -353.76\n",
      "No. Observations:                  84   AIC:                             711.5\n",
      "Df Residuals:                      82   BIC:                             716.4\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     41.5586      6.199      6.704      0.000      29.227      53.890\n",
      "Total_x        0.0426      0.085      0.500      0.618      -0.127       0.212\n",
      "==============================================================================\n",
      "Omnibus:                        3.497   Durbin-Watson:                   2.225\n",
      "Prob(Omnibus):                  0.174   Jarque-Bera (JB):                3.182\n",
      "Skew:                           0.477   Prob(JB):                        0.204\n",
      "Kurtosis:                       2.992   Cond. No.                         250.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Total_y ~ Total_x',\n",
    "                data=tt_[tt_.Group=='Human Creativity']).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b625321a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Total_y   R-squared:                       0.089\n",
      "Model:                            OLS   Adj. R-squared:                  0.031\n",
      "Method:                 Least Squares   F-statistic:                     1.532\n",
      "Date:                Fri, 08 Nov 2024   Prob (F-statistic):              0.189\n",
      "Time:                        23:11:40   Log-Likelihood:                -349.96\n",
      "No. Observations:                  84   AIC:                             711.9\n",
      "Df Residuals:                      78   BIC:                             726.5\n",
      "Df Model:                           5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     61.0138     19.617      3.110      0.003      21.958     100.069\n",
      "Total_x        0.0049      0.087      0.056      0.956      -0.169       0.178\n",
      "DAT           -0.1340      0.202     -0.663      0.509      -0.536       0.268\n",
      "Experience    -6.4829      2.785     -2.328      0.023     -12.028      -0.938\n",
      "Ability        5.9990      2.883      2.081      0.041       0.260      11.738\n",
      "English       -2.4920      5.069     -0.492      0.624     -12.583       7.599\n",
      "==============================================================================\n",
      "Omnibus:                        3.882   Durbin-Watson:                   2.346\n",
      "Prob(Omnibus):                  0.144   Jarque-Bera (JB):                3.851\n",
      "Skew:                           0.510   Prob(JB):                        0.146\n",
      "Kurtosis:                       2.753   Cond. No.                     1.21e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.21e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Total_y ~ Total_x + DAT + Experience + Ability + English',\n",
    "                data=tt_[tt_.Group=='Human Creativity']).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "50e9368c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Total_y   R-squared:                       0.219\n",
      "Model:                            OLS   Adj. R-squared:                  0.209\n",
      "Method:                 Least Squares   F-statistic:                     21.37\n",
      "Date:                Fri, 08 Nov 2024   Prob (F-statistic):           1.52e-05\n",
      "Time:                        23:12:48   Log-Likelihood:                -340.09\n",
      "No. Observations:                  78   AIC:                             684.2\n",
      "Df Residuals:                      76   BIC:                             688.9\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.9793      9.940      0.099      0.922     -18.817      20.776\n",
      "Total_x        0.6589      0.143      4.623      0.000       0.375       0.943\n",
      "==============================================================================\n",
      "Omnibus:                        7.248   Durbin-Watson:                   2.225\n",
      "Prob(Omnibus):                  0.027   Jarque-Bera (JB):                6.649\n",
      "Skew:                           0.680   Prob(JB):                       0.0360\n",
      "Kurtosis:                       3.442   Cond. No.                         319.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Total_y ~ Total_x',\n",
    "                data=tt_[tt_.Group=='Copilot']).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b7a6eb0c",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Total_y   R-squared:                       0.235\n",
      "Model:                            OLS   Adj. R-squared:                  0.182\n",
      "Method:                 Least Squares   F-statistic:                     4.425\n",
      "Date:                Fri, 08 Nov 2024   Prob (F-statistic):            0.00143\n",
      "Time:                        23:11:49   Log-Likelihood:                -339.30\n",
      "No. Observations:                  78   AIC:                             690.6\n",
      "Df Residuals:                      72   BIC:                             704.7\n",
      "Df Model:                           5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -6.4212     38.463     -0.167      0.868     -83.096      70.253\n",
      "Total_x        0.7012      0.153      4.574      0.000       0.396       1.007\n",
      "DAT           -0.1038      0.458     -0.227      0.821      -1.017       0.810\n",
      "Experience    -2.4580      3.619     -0.679      0.499      -9.673       4.757\n",
      "Ability        0.4708      4.047      0.116      0.908      -7.597       8.538\n",
      "English        5.9989      5.260      1.141      0.258      -4.486      16.484\n",
      "==============================================================================\n",
      "Omnibus:                        7.785   Durbin-Watson:                   2.155\n",
      "Prob(Omnibus):                  0.020   Jarque-Bera (JB):                7.227\n",
      "Skew:                           0.703   Prob(JB):                       0.0270\n",
      "Kurtosis:                       3.500   Cond. No.                     1.88e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.88e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Total_y ~ Total_x + DAT + Experience + Ability + English',\n",
    "                data=tt_[tt_.Group=='Copilot']).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a3dec41",
   "metadata": {},
   "source": [
    "# Table S.7: Overall Quality "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "e0d8f872",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Overall   R-squared:                       0.003\n",
      "Model:                            OLS   Adj. R-squared:                  0.001\n",
      "Method:                 Least Squares   F-statistic:                     1.448\n",
      "Date:                Fri, 08 Nov 2024   Prob (F-statistic):              0.236\n",
      "Time:                        01:20:52   Log-Likelihood:                -1881.4\n",
      "No. Observations:                1112   AIC:                             3769.\n",
      "Df Residuals:                    1109   BIC:                             3784.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===========================================================================================================================================\n",
      "                                                                              coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------------------------------------------------------------\n",
      "Intercept                                                                   4.9200      0.068     72.127      0.000       4.786       5.054\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Copilot]             -0.1518      0.098     -1.556      0.120      -0.343       0.040\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Human Creativity]    -0.0170      0.096     -0.178      0.859      -0.205       0.171\n",
      "==============================================================================\n",
      "Omnibus:                       53.081   Durbin-Watson:                   1.845\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               60.080\n",
      "Skew:                          -0.569   Prob(JB):                     8.99e-14\n",
      "Kurtosis:                       2.971   Cond. No.                         3.73\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Overall ~ C(Group, Treatment(reference=\"Human Confirmation\"))',\n",
    "                data=df[df.Day==1]).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "1d7dfd4d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Overall   R-squared:                       0.016\n",
      "Model:                            OLS   Adj. R-squared:                  0.011\n",
      "Method:                 Least Squares   F-statistic:                     2.974\n",
      "Date:                Fri, 08 Nov 2024   Prob (F-statistic):            0.00693\n",
      "Time:                        01:20:53   Log-Likelihood:                -1850.3\n",
      "No. Observations:                1096   AIC:                             3715.\n",
      "Df Residuals:                    1089   BIC:                             3750.\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===========================================================================================================================================\n",
      "                                                                              coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------------------------------------------------------------\n",
      "Intercept                                                                   3.5160      0.499      7.047      0.000       2.537       4.495\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Copilot]             -0.1443      0.099     -1.463      0.144      -0.338       0.049\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Human Creativity]     0.0061      0.098      0.062      0.951      -0.187       0.199\n",
      "DAT                                                                         0.0146      0.006      2.550      0.011       0.003       0.026\n",
      "Experience                                                                 -0.1594      0.066     -2.423      0.016      -0.288      -0.030\n",
      "Ability                                                                     0.1140      0.070      1.634      0.103      -0.023       0.251\n",
      "English                                                                     0.0866      0.097      0.895      0.371      -0.103       0.276\n",
      "==============================================================================\n",
      "Omnibus:                       54.482   Durbin-Watson:                   1.856\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               61.945\n",
      "Skew:                          -0.582   Prob(JB):                     3.54e-14\n",
      "Kurtosis:                       3.003   Cond. No.                     1.04e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.04e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Overall ~ C(Group, Treatment(reference=\"Human Confirmation\")) + DAT + Experience + Ability + English',\n",
    "                data=df[df.Day==1]).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "87c89eff",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Overall   R-squared:                       0.008\n",
      "Model:                            OLS   Adj. R-squared:                  0.007\n",
      "Method:                 Least Squares   F-statistic:                     4.559\n",
      "Date:                Fri, 08 Nov 2024   Prob (F-statistic):             0.0107\n",
      "Time:                        01:13:39   Log-Likelihood:                -1888.1\n",
      "No. Observations:                1084   AIC:                             3782.\n",
      "Df Residuals:                    1081   BIC:                             3797.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===========================================================================================================================================\n",
      "                                                                              coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------------------------------------------------------------\n",
      "Intercept                                                                   4.7670      0.074     64.672      0.000       4.622       4.912\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Copilot]              0.2628      0.104      2.535      0.011       0.059       0.466\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Human Creativity]     0.2780      0.103      2.703      0.007       0.076       0.480\n",
      "==============================================================================\n",
      "Omnibus:                       57.742   Durbin-Watson:                   1.938\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               66.238\n",
      "Skew:                          -0.603   Prob(JB):                     4.14e-15\n",
      "Kurtosis:                       2.884   Cond. No.                         3.78\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Overall ~ C(Group, Treatment(reference=\"Human Confirmation\"))',\n",
    "                data=df[df.Day==2]).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "e18be9cb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Overall   R-squared:                       0.014\n",
      "Model:                            OLS   Adj. R-squared:                  0.008\n",
      "Method:                 Least Squares   F-statistic:                     2.498\n",
      "Date:                Fri, 08 Nov 2024   Prob (F-statistic):             0.0210\n",
      "Time:                        01:13:27   Log-Likelihood:                -1857.7\n",
      "No. Observations:                1068   AIC:                             3729.\n",
      "Df Residuals:                    1061   BIC:                             3764.\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===========================================================================================================================================\n",
      "                                                                              coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------------------------------------------------------------\n",
      "Intercept                                                                   5.0622      0.528      9.583      0.000       4.026       6.099\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Copilot]              0.3158      0.105      3.006      0.003       0.110       0.522\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Human Creativity]     0.3376      0.106      3.196      0.001       0.130       0.545\n",
      "DAT                                                                         0.0007      0.006      0.109      0.913      -0.011       0.013\n",
      "Experience                                                                 -0.0805      0.071     -1.141      0.254      -0.219       0.058\n",
      "Ability                                                                    -0.0205      0.074     -0.276      0.783      -0.166       0.125\n",
      "English                                                                    -0.0831      0.101     -0.821      0.412      -0.282       0.116\n",
      "==============================================================================\n",
      "Omnibus:                       55.953   Durbin-Watson:                   1.950\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               64.016\n",
      "Skew:                          -0.597   Prob(JB):                     1.26e-14\n",
      "Kurtosis:                       2.885   Cond. No.                     1.03e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.03e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Overall ~ C(Group, Treatment(reference=\"Human Confirmation\")) + DAT + Experience + Ability + English',\n",
    "                data=df[df.Day==2]).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f6e9386",
   "metadata": {},
   "source": [
    "# Table S.8: Inequality in Overall Quality on Day 2 (Writing with AI)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "3ed251be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ID</th>\n",
       "      <th>Overall_x</th>\n",
       "      <th>Group</th>\n",
       "      <th>English</th>\n",
       "      <th>Experience</th>\n",
       "      <th>Ability</th>\n",
       "      <th>DAT</th>\n",
       "      <th>Overall_y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>4.5000</td>\n",
       "      <td>Human Creativity</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>86.81</td>\n",
       "      <td>4.250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>4.5000</td>\n",
       "      <td>Human Confirmation</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>89.58</td>\n",
       "      <td>6.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>3.7500</td>\n",
       "      <td>Human Creativity</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>52.20</td>\n",
       "      <td>3.750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5</td>\n",
       "      <td>5.2500</td>\n",
       "      <td>Human Confirmation</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>74.41</td>\n",
       "      <td>4.250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>7</td>\n",
       "      <td>5.0000</td>\n",
       "      <td>Human Creativity</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>91.64</td>\n",
       "      <td>4.750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>273</th>\n",
       "      <td>291</td>\n",
       "      <td>5.2500</td>\n",
       "      <td>Copilot</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>90.71</td>\n",
       "      <td>4.250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>274</th>\n",
       "      <td>292</td>\n",
       "      <td>5.5000</td>\n",
       "      <td>Human Creativity</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>75.07</td>\n",
       "      <td>5.250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>275</th>\n",
       "      <td>293</td>\n",
       "      <td>5.4375</td>\n",
       "      <td>Human Confirmation</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>80.36</td>\n",
       "      <td>5.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>276</th>\n",
       "      <td>294</td>\n",
       "      <td>4.5000</td>\n",
       "      <td>Copilot</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>87.08</td>\n",
       "      <td>3.875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>277</th>\n",
       "      <td>295</td>\n",
       "      <td>4.5000</td>\n",
       "      <td>Human Creativity</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>74.63</td>\n",
       "      <td>5.250</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>278 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      ID  Overall_x               Group  English  Experience  Ability    DAT  \\\n",
       "0      1     4.5000    Human Creativity      3.0         1.0      2.0  86.81   \n",
       "1      2     4.5000  Human Confirmation      2.0         1.0      1.0  89.58   \n",
       "2      4     3.7500    Human Creativity      3.0         1.0      2.0  52.20   \n",
       "3      5     5.2500  Human Confirmation      2.0         2.0      1.0  74.41   \n",
       "4      7     5.0000    Human Creativity      3.0         1.0      1.0  91.64   \n",
       "..   ...        ...                 ...      ...         ...      ...    ...   \n",
       "273  291     5.2500             Copilot      3.0         2.0      3.0  90.71   \n",
       "274  292     5.5000    Human Creativity      3.0         1.0      2.0  75.07   \n",
       "275  293     5.4375  Human Confirmation      3.0         1.0      1.0  80.36   \n",
       "276  294     4.5000             Copilot      3.0         3.0      2.0  87.08   \n",
       "277  295     4.5000    Human Creativity      2.0         1.0      1.0  74.63   \n",
       "\n",
       "     Overall_y  \n",
       "0        4.250  \n",
       "1        6.000  \n",
       "2        3.750  \n",
       "3        4.250  \n",
       "4        4.750  \n",
       "..         ...  \n",
       "273      4.250  \n",
       "274      5.250  \n",
       "275      5.000  \n",
       "276      3.875  \n",
       "277      5.250  \n",
       "\n",
       "[278 rows x 8 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t1 = df[df.Day == 1]\n",
    "t2 = df[df.Day == 2]\n",
    "\n",
    "t1_ = t1.groupby(by='ID')['Overall'].mean().reset_index()\n",
    "t1_ = pd.merge(t1_, t1[['ID', 'Group', 'English', 'Experience', 'Ability', 'DAT']], on=['ID']).drop_duplicates(keep='first').reset_index(drop=True)\n",
    "t2_ = t2.groupby(by='ID')['Overall'].mean().reset_index()\n",
    "t2_ = pd.merge(t2_, t2[['ID', 'Group']], on=['ID']).drop_duplicates(keep='first').reset_index(drop=True)\n",
    "tt_ = pd.merge(t1_, t2_, on=['ID', 'Group'], how='left')\n",
    "\n",
    "tt_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "1f7f4606",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:              Overall_y   R-squared:                       0.002\n",
      "Model:                            OLS   Adj. R-squared:                 -0.010\n",
      "Method:                 Least Squares   F-statistic:                    0.1891\n",
      "Date:                Fri, 08 Nov 2024   Prob (F-statistic):              0.665\n",
      "Time:                        23:36:44   Log-Likelihood:                -99.210\n",
      "No. Observations:                  86   AIC:                             202.4\n",
      "Df Residuals:                      84   BIC:                             207.3\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      4.5196      0.570      7.935      0.000       3.387       5.652\n",
      "Overall_x      0.0497      0.114      0.435      0.665      -0.178       0.277\n",
      "==============================================================================\n",
      "Omnibus:                        3.791   Durbin-Watson:                   1.994\n",
      "Prob(Omnibus):                  0.150   Jarque-Bera (JB):                2.435\n",
      "Skew:                          -0.213   Prob(JB):                        0.296\n",
      "Kurtosis:                       2.294   Cond. No.                         35.3\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Overall_y ~ Overall_x',\n",
    "                data=tt_[tt_.Group=='Human Confirmation']).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "456cd786",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:              Overall_y   R-squared:                       0.075\n",
      "Model:                            OLS   Adj. R-squared:                  0.015\n",
      "Method:                 Least Squares   F-statistic:                     1.244\n",
      "Date:                Fri, 08 Nov 2024   Prob (F-statistic):              0.297\n",
      "Time:                        23:36:48   Log-Likelihood:                -91.217\n",
      "No. Observations:                  83   AIC:                             194.4\n",
      "Df Residuals:                      77   BIC:                             208.9\n",
      "Df Model:                           5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      3.6482      1.321      2.762      0.007       1.018       6.278\n",
      "Overall_x      0.0864      0.114      0.757      0.452      -0.141       0.314\n",
      "DAT            0.0112      0.014      0.805      0.423      -0.017       0.039\n",
      "Experience    -0.1429      0.155     -0.924      0.358      -0.451       0.165\n",
      "Ability       -0.1974      0.151     -1.304      0.196      -0.499       0.104\n",
      "English        0.1158      0.183      0.632      0.529      -0.249       0.481\n",
      "==============================================================================\n",
      "Omnibus:                        6.396   Durbin-Watson:                   2.125\n",
      "Prob(Omnibus):                  0.041   Jarque-Bera (JB):                3.476\n",
      "Skew:                          -0.283   Prob(JB):                        0.176\n",
      "Kurtosis:                       2.173   Cond. No.                     1.33e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.33e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Overall_y ~ Overall_x + DAT + Experience + Ability + English',\n",
    "                data=tt_[tt_.Group=='Human Confirmation']).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "96a9527d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:              Overall_y   R-squared:                       0.057\n",
      "Model:                            OLS   Adj. R-squared:                  0.046\n",
      "Method:                 Least Squares   F-statistic:                     5.298\n",
      "Date:                Fri, 08 Nov 2024   Prob (F-statistic):             0.0237\n",
      "Time:                        23:36:53   Log-Likelihood:                -83.806\n",
      "No. Observations:                  90   AIC:                             171.6\n",
      "Df Residuals:                      88   BIC:                             176.6\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      4.0526      0.438      9.254      0.000       3.182       4.923\n",
      "Overall_x      0.2016      0.088      2.302      0.024       0.028       0.376\n",
      "==============================================================================\n",
      "Omnibus:                        4.899   Durbin-Watson:                   1.976\n",
      "Prob(Omnibus):                  0.086   Jarque-Bera (JB):                4.370\n",
      "Skew:                          -0.531   Prob(JB):                        0.112\n",
      "Kurtosis:                       3.197   Cond. No.                         34.8\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Overall_y ~ Overall_x',\n",
    "                data=tt_[tt_.Group=='Human Creativity']).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "b5ea0b7c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:              Overall_y   R-squared:                       0.123\n",
      "Model:                            OLS   Adj. R-squared:                  0.071\n",
      "Method:                 Least Squares   F-statistic:                     2.357\n",
      "Date:                Fri, 08 Nov 2024   Prob (F-statistic):             0.0471\n",
      "Time:                        23:36:58   Log-Likelihood:                -80.528\n",
      "No. Observations:                  90   AIC:                             173.1\n",
      "Df Residuals:                      84   BIC:                             188.1\n",
      "Df Model:                           5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      5.3392      0.781      6.838      0.000       3.786       6.892\n",
      "Overall_x      0.2442      0.093      2.621      0.010       0.059       0.430\n",
      "DAT           -0.0054      0.008     -0.720      0.474      -0.020       0.010\n",
      "Experience     0.0746      0.103      0.725      0.470      -0.130       0.279\n",
      "Ability       -0.1255      0.108     -1.167      0.247      -0.339       0.088\n",
      "English       -0.3284      0.184     -1.788      0.077      -0.694       0.037\n",
      "==============================================================================\n",
      "Omnibus:                        3.803   Durbin-Watson:                   1.972\n",
      "Prob(Omnibus):                  0.149   Jarque-Bera (JB):                3.254\n",
      "Skew:                          -0.457   Prob(JB):                        0.197\n",
      "Kurtosis:                       3.181   Cond. No.                     1.00e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large,  1e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Overall_y ~ Overall_x + DAT + Experience + Ability + English',\n",
    "                data=tt_[tt_.Group=='Human Creativity']).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "d9b9bf3e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:              Overall_y   R-squared:                       0.040\n",
      "Model:                            OLS   Adj. R-squared:                  0.029\n",
      "Method:                 Least Squares   F-statistic:                     3.564\n",
      "Date:                Fri, 08 Nov 2024   Prob (F-statistic):             0.0624\n",
      "Time:                        23:37:02   Log-Likelihood:                -90.200\n",
      "No. Observations:                  88   AIC:                             184.4\n",
      "Df Residuals:                      86   BIC:                             189.4\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      4.1926      0.454      9.230      0.000       3.290       5.096\n",
      "Overall_x      0.1774      0.094      1.888      0.062      -0.009       0.364\n",
      "==============================================================================\n",
      "Omnibus:                        9.771   Durbin-Watson:                   1.883\n",
      "Prob(Omnibus):                  0.008   Jarque-Bera (JB):                9.613\n",
      "Skew:                          -0.744   Prob(JB):                      0.00818\n",
      "Kurtosis:                       3.638   Cond. No.                         31.5\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Overall_y ~ Overall_x',\n",
    "                data=tt_[tt_.Group=='Copilot']).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "51af6a4a",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:              Overall_y   R-squared:                       0.106\n",
      "Model:                            OLS   Adj. R-squared:                  0.052\n",
      "Method:                 Least Squares   F-statistic:                     1.950\n",
      "Date:                Fri, 08 Nov 2024   Prob (F-statistic):             0.0948\n",
      "Time:                        23:37:08   Log-Likelihood:                -87.043\n",
      "No. Observations:                  88   AIC:                             186.1\n",
      "Df Residuals:                      82   BIC:                             200.9\n",
      "Df Model:                           5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      4.9040      1.171      4.187      0.000       2.574       7.234\n",
      "Overall_x      0.2069      0.095      2.170      0.033       0.017       0.397\n",
      "DAT           -0.0059      0.014     -0.419      0.677      -0.034       0.022\n",
      "Experience    -0.1106      0.124     -0.894      0.374      -0.357       0.136\n",
      "Ability        0.2695      0.133      2.023      0.046       0.005       0.535\n",
      "English       -0.2545      0.173     -1.472      0.145      -0.598       0.089\n",
      "==============================================================================\n",
      "Omnibus:                        6.688   Durbin-Watson:                   1.903\n",
      "Prob(Omnibus):                  0.035   Jarque-Bera (JB):                6.221\n",
      "Skew:                          -0.636   Prob(JB):                       0.0446\n",
      "Kurtosis:                       3.278   Cond. No.                     1.36e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.36e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Overall_y ~ Overall_x + DAT + Experience + Ability + English',\n",
    "                data=tt_[tt_.Group=='Copilot']).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee134bf8",
   "metadata": {},
   "source": [
    "# Table S.9: Inequality in Overall Quality by DAT Score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "49733db6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Overall   R-squared:                       0.007\n",
      "Model:                            OLS   Adj. R-squared:                  0.006\n",
      "Method:                 Least Squares   F-statistic:                     7.565\n",
      "Date:                Fri, 08 Nov 2024   Prob (F-statistic):            0.00605\n",
      "Time:                        23:57:04   Log-Likelihood:                -1855.4\n",
      "No. Observations:                1096   AIC:                             3715.\n",
      "Df Residuals:                    1094   BIC:                             3725.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      3.6088      0.460      7.852      0.000       2.707       4.511\n",
      "DAT            0.0153      0.006      2.751      0.006       0.004       0.026\n",
      "==============================================================================\n",
      "Omnibus:                       52.896   Durbin-Watson:                   1.859\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               59.937\n",
      "Skew:                          -0.573   Prob(JB):                     9.66e-14\n",
      "Kurtosis:                       2.978   Cond. No.                         955.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Overall ~ DAT',\n",
    "                data=df[df.Day==1]).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "2462c546",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Overall   R-squared:                       0.013\n",
      "Model:                            OLS   Adj. R-squared:                  0.010\n",
      "Method:                 Least Squares   F-statistic:                     3.708\n",
      "Date:                Fri, 08 Nov 2024   Prob (F-statistic):            0.00526\n",
      "Time:                        23:58:37   Log-Likelihood:                -1851.8\n",
      "No. Observations:                1096   AIC:                             3714.\n",
      "Df Residuals:                    1091   BIC:                             3739.\n",
      "Df Model:                           4                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      3.5091      0.496      7.068      0.000       2.535       4.483\n",
      "DAT            0.0139      0.006      2.455      0.014       0.003       0.025\n",
      "Experience    -0.1673      0.066     -2.549      0.011      -0.296      -0.039\n",
      "Ability        0.1144      0.070      1.641      0.101      -0.022       0.251\n",
      "English        0.0961      0.096      1.005      0.315      -0.091       0.284\n",
      "==============================================================================\n",
      "Omnibus:                       54.867   Durbin-Watson:                   1.855\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               62.435\n",
      "Skew:                          -0.585   Prob(JB):                     2.77e-14\n",
      "Kurtosis:                       3.008   Cond. No.                     1.04e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.04e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Overall ~ DAT + Experience + Ability + English',\n",
    "                data=df[df.Day==1]).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "400310ba",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Overall   R-squared:                       0.000\n",
      "Model:                            OLS   Adj. R-squared:                 -0.001\n",
      "Method:                 Least Squares   F-statistic:                   0.06334\n",
      "Date:                Sat, 09 Nov 2024   Prob (F-statistic):              0.801\n",
      "Time:                        00:00:45   Log-Likelihood:                -1865.1\n",
      "No. Observations:                1068   AIC:                             3734.\n",
      "Df Residuals:                    1066   BIC:                             3744.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      5.0645      0.491     10.321      0.000       4.102       6.027\n",
      "DAT           -0.0015      0.006     -0.252      0.801      -0.013       0.010\n",
      "==============================================================================\n",
      "Omnibus:                       61.476   Durbin-Watson:                   1.949\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               71.294\n",
      "Skew:                          -0.630   Prob(JB):                     3.30e-16\n",
      "Kurtosis:                       2.872   Cond. No.                         953.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Overall ~ DAT',\n",
    "                data=df[df.Day==2]).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "598997b2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Overall   R-squared:                       0.002\n",
      "Model:                            OLS   Adj. R-squared:                 -0.002\n",
      "Method:                 Least Squares   F-statistic:                    0.5577\n",
      "Date:                Sat, 09 Nov 2024   Prob (F-statistic):              0.693\n",
      "Time:                        00:01:42   Log-Likelihood:                -1864.1\n",
      "No. Observations:                1068   AIC:                             3738.\n",
      "Df Residuals:                    1063   BIC:                             3763.\n",
      "Df Model:                           4                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      5.2458      0.528      9.940      0.000       4.210       6.281\n",
      "DAT           -0.0005      0.006     -0.085      0.933      -0.012       0.011\n",
      "Experience    -0.0762      0.071     -1.078      0.281      -0.215       0.062\n",
      "Ability       -0.0049      0.075     -0.066      0.948      -0.151       0.141\n",
      "English       -0.0469      0.101     -0.466      0.641      -0.244       0.151\n",
      "==============================================================================\n",
      "Omnibus:                       60.992   Durbin-Watson:                   1.954\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               70.629\n",
      "Skew:                          -0.627   Prob(JB):                     4.60e-16\n",
      "Kurtosis:                       2.869   Cond. No.                     1.03e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.03e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Overall ~ DAT + Experience + Ability + English',\n",
    "                data=df[df.Day==2]).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ae8f00b",
   "metadata": {},
   "source": [
    "# Table S.10: Comparison of Process Satisfaction Scores Between Day 1 and Day 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "a56340a4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:           Satisfaction   R-squared:                       0.052\n",
      "Model:                            OLS   Adj. R-squared:                  0.021\n",
      "Method:                 Least Squares   F-statistic:                     1.669\n",
      "Date:                Sun, 17 Nov 2024   Prob (F-statistic):              0.145\n",
      "Time:                        16:29:46   Log-Likelihood:                -290.90\n",
      "No. Observations:                 158   AIC:                             593.8\n",
      "Df Residuals:                     152   BIC:                             612.2\n",
      "Df Model:                           5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      4.6177      1.713      2.695      0.008       1.233       8.002\n",
      "Day           -0.0507      0.248     -0.204      0.838      -0.541       0.440\n",
      "DAT           -0.0202      0.020     -1.009      0.314      -0.060       0.019\n",
      "Experience     0.3688      0.237      1.558      0.121      -0.099       0.837\n",
      "Ability        0.0907      0.221      0.411      0.682      -0.345       0.527\n",
      "English        0.3813      0.278      1.373      0.172      -0.167       0.930\n",
      "==============================================================================\n",
      "Omnibus:                        8.340   Durbin-Watson:                   1.939\n",
      "Prob(Omnibus):                  0.015   Jarque-Bera (JB):                8.690\n",
      "Skew:                          -0.550   Prob(JB):                       0.0130\n",
      "Kurtosis:                       2.667   Cond. No.                     1.15e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.15e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "tmp = df.groupby(by=['ID', 'Day'])[['Group', 'Satisfaction', 'Flexibility', 'Goal', 'Again', \n",
    "                                    'DAT', 'Ability', 'Experience', 'English']].first().reset_index()\n",
    "tmp['Day'] = tmp['Day'] - 1\n",
    "model = smf.ols('Satisfaction ~ Day + DAT + Experience + Ability + English',\n",
    "                data=tmp[tmp.Group=='Human Confirmation']).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "7c1b6777",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:           Satisfaction   R-squared:                       0.146\n",
      "Model:                            OLS   Adj. R-squared:                  0.122\n",
      "Method:                 Least Squares   F-statistic:                     5.936\n",
      "Date:                Sun, 17 Nov 2024   Prob (F-statistic):           4.30e-05\n",
      "Time:                        16:30:05   Log-Likelihood:                -315.98\n",
      "No. Observations:                 179   AIC:                             644.0\n",
      "Df Residuals:                     173   BIC:                             663.1\n",
      "Df Model:                           5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      3.6794      1.185      3.105      0.002       1.341       6.018\n",
      "Day            0.8584      0.215      3.991      0.000       0.434       1.283\n",
      "DAT            0.0097      0.012      0.790      0.430      -0.015       0.034\n",
      "Experience     0.4038      0.162      2.490      0.014       0.084       0.724\n",
      "Ability        0.2150      0.179      1.200      0.232      -0.139       0.569\n",
      "English       -0.3626      0.310     -1.170      0.244      -0.975       0.249\n",
      "==============================================================================\n",
      "Omnibus:                       13.412   Durbin-Watson:                   2.011\n",
      "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               15.001\n",
      "Skew:                          -0.707   Prob(JB):                     0.000553\n",
      "Kurtosis:                       2.890   Cond. No.                         912.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Satisfaction ~ Day + DAT + Experience + Ability + English',\n",
    "                data=tmp[tmp.Group=='Human Creativity']).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "e7b04123",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:           Satisfaction   R-squared:                       0.024\n",
      "Model:                            OLS   Adj. R-squared:                 -0.007\n",
      "Method:                 Least Squares   F-statistic:                    0.7771\n",
      "Date:                Sun, 17 Nov 2024   Prob (F-statistic):              0.568\n",
      "Time:                        16:30:13   Log-Likelihood:                -298.76\n",
      "No. Observations:                 167   AIC:                             609.5\n",
      "Df Residuals:                     161   BIC:                             628.2\n",
      "Df Model:                           5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      4.9857      1.871      2.664      0.009       1.290       8.681\n",
      "Day            0.4154      0.228      1.818      0.071      -0.036       0.867\n",
      "DAT            0.0035      0.022      0.156      0.876      -0.041       0.048\n",
      "Experience     0.0680      0.191      0.355      0.723      -0.310       0.446\n",
      "Ability       -0.0390      0.207     -0.188      0.851      -0.449       0.371\n",
      "English       -0.1700      0.266     -0.640      0.523      -0.695       0.355\n",
      "==============================================================================\n",
      "Omnibus:                       17.850   Durbin-Watson:                   1.838\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               21.123\n",
      "Skew:                          -0.871   Prob(JB):                     2.59e-05\n",
      "Kurtosis:                       3.008   Cond. No.                     1.37e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.37e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Satisfaction ~ Day + DAT + Experience + Ability + English',\n",
    "                data=tmp[tmp.Group=='Copilot']).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "5ed7f0b4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:            Flexibility   R-squared:                       0.077\n",
      "Model:                            OLS   Adj. R-squared:                  0.047\n",
      "Method:                 Least Squares   F-statistic:                     2.545\n",
      "Date:                Sun, 17 Nov 2024   Prob (F-statistic):             0.0304\n",
      "Time:                        16:41:40   Log-Likelihood:                -287.13\n",
      "No. Observations:                 158   AIC:                             586.3\n",
      "Df Residuals:                     152   BIC:                             604.6\n",
      "Df Model:                           5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      4.7974      1.673      2.868      0.005       1.493       8.102\n",
      "Day           -0.7975      0.242     -3.290      0.001      -1.276      -0.319\n",
      "DAT           -0.0014      0.020     -0.072      0.943      -0.040       0.037\n",
      "Experience     0.3301      0.231      1.428      0.155      -0.127       0.787\n",
      "Ability       -0.2524      0.216     -1.171      0.243      -0.678       0.173\n",
      "English        0.1274      0.271      0.470      0.639      -0.408       0.663\n",
      "==============================================================================\n",
      "Omnibus:                        5.468   Durbin-Watson:                   1.819\n",
      "Prob(Omnibus):                  0.065   Jarque-Bera (JB):                5.576\n",
      "Skew:                          -0.436   Prob(JB):                       0.0615\n",
      "Kurtosis:                       2.707   Cond. No.                     1.15e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.15e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Flexibility ~ Day + DAT + Experience + Ability + English',\n",
    "                data=tmp[tmp.Group=='Human Confirmation']).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "53e174c2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:            Flexibility   R-squared:                       0.045\n",
      "Model:                            OLS   Adj. R-squared:                  0.018\n",
      "Method:                 Least Squares   F-statistic:                     1.638\n",
      "Date:                Sun, 17 Nov 2024   Prob (F-statistic):              0.152\n",
      "Time:                        16:41:41   Log-Likelihood:                -314.10\n",
      "No. Observations:                 179   AIC:                             640.2\n",
      "Df Residuals:                     173   BIC:                             659.3\n",
      "Df Model:                           5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      2.7136      1.172      2.314      0.022       0.399       5.028\n",
      "Day           -0.0050      0.213     -0.024      0.981      -0.425       0.415\n",
      "DAT            0.0259      0.012      2.127      0.035       0.002       0.050\n",
      "Experience     0.1163      0.160      0.724      0.470      -0.200       0.433\n",
      "Ability        0.1859      0.177      1.048      0.296      -0.164       0.536\n",
      "English       -0.1231      0.307     -0.401      0.689      -0.729       0.482\n",
      "==============================================================================\n",
      "Omnibus:                       11.702   Durbin-Watson:                   2.185\n",
      "Prob(Omnibus):                  0.003   Jarque-Bera (JB):               12.821\n",
      "Skew:                          -0.652   Prob(JB):                      0.00164\n",
      "Kurtosis:                       2.873   Cond. No.                         912.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Flexibility ~ Day + DAT + Experience + Ability + English',\n",
    "                data=tmp[tmp.Group=='Human Creativity']).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "c7571873",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:            Flexibility   R-squared:                       0.012\n",
      "Model:                            OLS   Adj. R-squared:                 -0.019\n",
      "Method:                 Least Squares   F-statistic:                    0.3752\n",
      "Date:                Sun, 17 Nov 2024   Prob (F-statistic):              0.865\n",
      "Time:                        16:41:41   Log-Likelihood:                -293.27\n",
      "No. Observations:                 167   AIC:                             598.5\n",
      "Df Residuals:                     161   BIC:                             617.3\n",
      "Df Model:                           5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      6.4340      1.811      3.553      0.001       2.858      10.010\n",
      "Day            0.0484      0.221      0.219      0.827      -0.388       0.485\n",
      "DAT           -0.0101      0.022     -0.468      0.640      -0.053       0.033\n",
      "Experience    -0.1232      0.185     -0.665      0.507      -0.489       0.242\n",
      "Ability        0.1294      0.201      0.645      0.520      -0.267       0.526\n",
      "English       -0.1961      0.257     -0.763      0.447      -0.704       0.312\n",
      "==============================================================================\n",
      "Omnibus:                       13.005   Durbin-Watson:                   2.147\n",
      "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               14.104\n",
      "Skew:                          -0.685   Prob(JB):                     0.000866\n",
      "Kurtosis:                       2.616   Cond. No.                     1.37e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.37e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Flexibility ~ Day + DAT + Experience + Ability + English',\n",
    "                data=tmp[tmp.Group=='Copilot']).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "7f5c63dc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   Goal   R-squared:                       0.036\n",
      "Model:                            OLS   Adj. R-squared:                  0.004\n",
      "Method:                 Least Squares   F-statistic:                     1.127\n",
      "Date:                Sun, 17 Nov 2024   Prob (F-statistic):              0.349\n",
      "Time:                        16:45:40   Log-Likelihood:                -302.02\n",
      "No. Observations:                 158   AIC:                             616.0\n",
      "Df Residuals:                     152   BIC:                             634.4\n",
      "Df Model:                           5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      5.9629      1.838      3.244      0.001       2.331       9.594\n",
      "Day           -0.0715      0.266     -0.268      0.789      -0.598       0.455\n",
      "DAT           -0.0315      0.021     -1.464      0.145      -0.074       0.011\n",
      "Experience     0.3934      0.254      1.548      0.124      -0.109       0.895\n",
      "Ability       -0.1334      0.237     -0.563      0.574      -0.601       0.335\n",
      "English        0.2735      0.298      0.918      0.360      -0.315       0.862\n",
      "==============================================================================\n",
      "Omnibus:                       14.108   Durbin-Watson:                   1.868\n",
      "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               10.013\n",
      "Skew:                          -0.495   Prob(JB):                      0.00670\n",
      "Kurtosis:                       2.264   Cond. No.                     1.15e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.15e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Goal ~ Day + DAT + Experience + Ability + English',\n",
    "                data=tmp[tmp.Group=='Human Confirmation']).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "f1a98e89",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   Goal   R-squared:                       0.111\n",
      "Model:                            OLS   Adj. R-squared:                  0.085\n",
      "Method:                 Least Squares   F-statistic:                     4.299\n",
      "Date:                Sun, 17 Nov 2024   Prob (F-statistic):            0.00104\n",
      "Time:                        16:45:40   Log-Likelihood:                -324.24\n",
      "No. Observations:                 179   AIC:                             660.5\n",
      "Df Residuals:                     173   BIC:                             679.6\n",
      "Df Model:                           5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      3.8592      1.241      3.110      0.002       1.410       6.308\n",
      "Day            0.8491      0.225      3.769      0.000       0.404       1.294\n",
      "DAT            0.0051      0.013      0.399      0.691      -0.020       0.031\n",
      "Experience     0.3015      0.170      1.775      0.078      -0.034       0.637\n",
      "Ability        0.1822      0.188      0.970      0.333      -0.188       0.553\n",
      "English       -0.2751      0.325     -0.847      0.398      -0.916       0.366\n",
      "==============================================================================\n",
      "Omnibus:                       10.164   Durbin-Watson:                   2.115\n",
      "Prob(Omnibus):                  0.006   Jarque-Bera (JB):                9.923\n",
      "Skew:                          -0.527   Prob(JB):                      0.00700\n",
      "Kurtosis:                       2.529   Cond. No.                         912.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Goal ~ Day + DAT + Experience + Ability + English',\n",
    "                data=tmp[tmp.Group=='Human Creativity']).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "52f37c5e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   Goal   R-squared:                       0.093\n",
      "Model:                            OLS   Adj. R-squared:                  0.065\n",
      "Method:                 Least Squares   F-statistic:                     3.316\n",
      "Date:                Sun, 17 Nov 2024   Prob (F-statistic):            0.00706\n",
      "Time:                        16:45:40   Log-Likelihood:                -289.58\n",
      "No. Observations:                 167   AIC:                             591.2\n",
      "Df Residuals:                     161   BIC:                             609.9\n",
      "Df Model:                           5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      4.0169      1.771      2.268      0.025       0.519       7.515\n",
      "Day            0.8548      0.216      3.952      0.000       0.428       1.282\n",
      "DAT            0.0108      0.021      0.508      0.612      -0.031       0.053\n",
      "Experience    -0.0118      0.181     -0.065      0.948      -0.369       0.346\n",
      "Ability       -0.0922      0.196     -0.470      0.639      -0.480       0.296\n",
      "English       -0.0578      0.251     -0.230      0.819      -0.554       0.439\n",
      "==============================================================================\n",
      "Omnibus:                       18.168   Durbin-Watson:                   2.177\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               21.133\n",
      "Skew:                          -0.866   Prob(JB):                     2.58e-05\n",
      "Kurtosis:                       3.191   Cond. No.                     1.37e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.37e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Goal ~ Day + DAT + Experience + Ability + English',\n",
    "                data=tmp[tmp.Group=='Copilot']).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "efc744a8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  Again   R-squared:                       0.038\n",
      "Model:                            OLS   Adj. R-squared:                  0.007\n",
      "Method:                 Least Squares   F-statistic:                     1.213\n",
      "Date:                Sun, 17 Nov 2024   Prob (F-statistic):              0.306\n",
      "Time:                        16:58:29   Log-Likelihood:                -100.15\n",
      "No. Observations:                 158   AIC:                             212.3\n",
      "Df Residuals:                     152   BIC:                             230.7\n",
      "Df Model:                           5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.9169      0.512      1.790      0.075      -0.095       1.929\n",
      "Day           -0.1320      0.074     -1.779      0.077      -0.279       0.015\n",
      "DAT           -0.0043      0.006     -0.713      0.477      -0.016       0.008\n",
      "Experience     0.0420      0.071      0.593      0.554      -0.098       0.182\n",
      "Ability       -0.0761      0.066     -1.153      0.251      -0.206       0.054\n",
      "English        0.0945      0.083      1.138      0.257      -0.070       0.259\n",
      "==============================================================================\n",
      "Omnibus:                      100.996   Durbin-Watson:                   1.833\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               25.406\n",
      "Skew:                          -0.757   Prob(JB):                     3.04e-06\n",
      "Kurtosis:                       1.748   Cond. No.                     1.15e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.15e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Again ~ Day + DAT + Experience + Ability + English',\n",
    "                data=tmp[tmp.Group=='Human Confirmation']).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "bbe4b563",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  Again   R-squared:                       0.083\n",
      "Model:                            OLS   Adj. R-squared:                  0.056\n",
      "Method:                 Least Squares   F-statistic:                     3.123\n",
      "Date:                Sun, 17 Nov 2024   Prob (F-statistic):             0.0100\n",
      "Time:                        16:45:41   Log-Likelihood:                -102.79\n",
      "No. Observations:                 179   AIC:                             217.6\n",
      "Df Residuals:                     173   BIC:                             236.7\n",
      "Df Model:                           5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.9014      0.360      2.503      0.013       0.191       1.612\n",
      "Day            0.1510      0.065      2.310      0.022       0.022       0.280\n",
      "DAT           -0.0017      0.004     -0.460      0.646      -0.009       0.006\n",
      "Experience     0.1392      0.049      2.824      0.005       0.042       0.236\n",
      "Ability       -0.0217      0.054     -0.398      0.691      -0.129       0.086\n",
      "English       -0.1051      0.094     -1.115      0.266      -0.291       0.081\n",
      "==============================================================================\n",
      "Omnibus:                       42.820   Durbin-Watson:                   1.884\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               27.165\n",
      "Skew:                          -0.823   Prob(JB):                     1.26e-06\n",
      "Kurtosis:                       2.033   Cond. No.                         912.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Again ~ Day + DAT + Experience + Ability + English',\n",
    "                data=tmp[tmp.Group=='Human Creativity']).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "75df5f87",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  Again   R-squared:                       0.037\n",
      "Model:                            OLS   Adj. R-squared:                  0.007\n",
      "Method:                 Least Squares   F-statistic:                     1.249\n",
      "Date:                Sun, 17 Nov 2024   Prob (F-statistic):              0.289\n",
      "Time:                        16:45:41   Log-Likelihood:                -92.994\n",
      "No. Observations:                 167   AIC:                             198.0\n",
      "Df Residuals:                     161   BIC:                             216.7\n",
      "Df Model:                           5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.2039      0.546      0.374      0.709      -0.874       1.282\n",
      "Day            0.1484      0.067      2.227      0.027       0.017       0.280\n",
      "DAT            0.0035      0.007      0.541      0.589      -0.009       0.016\n",
      "Experience    -0.0182      0.056     -0.326      0.745      -0.128       0.092\n",
      "Ability        0.0270      0.061      0.447      0.655      -0.092       0.147\n",
      "English        0.0594      0.077      0.766      0.445      -0.094       0.212\n",
      "==============================================================================\n",
      "Omnibus:                       29.290   Durbin-Watson:                   2.105\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               37.817\n",
      "Skew:                          -1.138   Prob(JB):                     6.14e-09\n",
      "Kurtosis:                       2.491   Cond. No.                     1.37e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.37e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Again ~ Day + DAT + Experience + Ability + English',\n",
    "                data=tmp[tmp.Group=='Copilot']).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2c20e86",
   "metadata": {},
   "source": [
    "# Table S.11: Process Satisfaction Among Groups on Day 2 (Writing with AI)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "3a15250e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:           Satisfaction   R-squared:                       0.058\n",
      "Model:                            OLS   Adj. R-squared:                  0.034\n",
      "Method:                 Least Squares   F-statistic:                     2.448\n",
      "Date:                Sun, 17 Nov 2024   Prob (F-statistic):             0.0257\n",
      "Time:                        17:26:16   Log-Likelihood:                -457.07\n",
      "No. Observations:                 246   AIC:                             928.1\n",
      "Df Residuals:                     239   BIC:                             952.7\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===========================================================================================================================================\n",
      "                                                                              coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------------------------------------------------------------\n",
      "Intercept                                                                   5.8092      1.236      4.701      0.000       3.375       8.244\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Copilot]              0.5793      0.251      2.304      0.022       0.084       1.075\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Human Creativity]     0.6766      0.250      2.706      0.007       0.184       1.169\n",
      "DAT                                                                        -0.0146      0.014     -1.018      0.310      -0.043       0.014\n",
      "Experience                                                                  0.3575      0.164      2.173      0.031       0.033       0.682\n",
      "Ability                                                                    -0.1993      0.173     -1.152      0.250      -0.540       0.141\n",
      "English                                                                    -0.0438      0.244     -0.180      0.858      -0.524       0.436\n",
      "==============================================================================\n",
      "Omnibus:                       23.173   Durbin-Watson:                   1.981\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               27.690\n",
      "Skew:                          -0.812   Prob(JB):                     9.71e-07\n",
      "Kurtosis:                       2.750   Cond. No.                     1.02e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.02e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "tmp = df.groupby(by=['ID', 'Day'])[['Group', 'Satisfaction', 'Flexibility', 'Goal', 'Again', \n",
    "                                    'DAT', 'Ability', 'Experience', 'English']].first().reset_index()\n",
    "model = smf.ols('Satisfaction ~ C(Group, Treatment(reference=\"Human Confirmation\")) + DAT + Experience + Ability + English',\n",
    "                data=tmp[tmp.Day==2]).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "85a557bd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:            Flexibility   R-squared:                       0.071\n",
      "Model:                            OLS   Adj. R-squared:                  0.048\n",
      "Method:                 Least Squares   F-statistic:                     3.055\n",
      "Date:                Sun, 17 Nov 2024   Prob (F-statistic):            0.00673\n",
      "Time:                        17:27:00   Log-Likelihood:                -458.75\n",
      "No. Observations:                 246   AIC:                             931.5\n",
      "Df Residuals:                     239   BIC:                             956.0\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===========================================================================================================================================\n",
      "                                                                              coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------------------------------------------------------------\n",
      "Intercept                                                                   4.7968      1.244      3.855      0.000       2.345       7.248\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Copilot]              0.8692      0.253      3.433      0.001       0.370       1.368\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Human Creativity]     0.7848      0.252      3.117      0.002       0.289       1.281\n",
      "DAT                                                                         0.0037      0.014      0.257      0.797      -0.025       0.032\n",
      "Experience                                                                  0.1889      0.166      1.140      0.255      -0.137       0.515\n",
      "Ability                                                                    -0.3667      0.174     -2.106      0.036      -0.710      -0.024\n",
      "English                                                                    -0.1628      0.245     -0.663      0.508      -0.646       0.321\n",
      "==============================================================================\n",
      "Omnibus:                       19.472   Durbin-Watson:                   1.982\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               14.154\n",
      "Skew:                          -0.475   Prob(JB):                     0.000844\n",
      "Kurtosis:                       2.309   Cond. No.                     1.02e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.02e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Flexibility ~ C(Group, Treatment(reference=\"Human Confirmation\")) + DAT + Experience + Ability + English',\n",
    "                data=tmp[tmp.Day==2]).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "c7c15646",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   Goal   R-squared:                       0.095\n",
      "Model:                            OLS   Adj. R-squared:                  0.072\n",
      "Method:                 Least Squares   F-statistic:                     4.161\n",
      "Date:                Sun, 17 Nov 2024   Prob (F-statistic):           0.000535\n",
      "Time:                        17:28:48   Log-Likelihood:                -456.32\n",
      "No. Observations:                 246   AIC:                             926.6\n",
      "Df Residuals:                     239   BIC:                             951.2\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===========================================================================================================================================\n",
      "                                                                              coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------------------------------------------------------------\n",
      "Intercept                                                                   6.0296      1.232      4.894      0.000       3.602       8.457\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Copilot]              1.0316      0.251      4.115      0.000       0.538       1.525\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Human Creativity]     0.8023      0.249      3.219      0.001       0.311       1.293\n",
      "DAT                                                                        -0.0109      0.014     -0.760      0.448      -0.039       0.017\n",
      "Experience                                                                  0.1191      0.164      0.727      0.468      -0.204       0.442\n",
      "Ability                                                                    -0.4136      0.172     -2.398      0.017      -0.753      -0.074\n",
      "English                                                                    -0.0546      0.243     -0.224      0.823      -0.533       0.424\n",
      "==============================================================================\n",
      "Omnibus:                       20.992   Durbin-Watson:                   2.132\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               24.657\n",
      "Skew:                          -0.768   Prob(JB):                     4.42e-06\n",
      "Kurtosis:                       2.786   Cond. No.                     1.02e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.02e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Goal ~ C(Group, Treatment(reference=\"Human Confirmation\")) + DAT + Experience + Ability + English',\n",
    "                data=tmp[tmp.Day==2]).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "fb7379b1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  Again   R-squared:                       0.084\n",
      "Model:                            OLS   Adj. R-squared:                  0.061\n",
      "Method:                 Least Squares   F-statistic:                     3.663\n",
      "Date:                Sun, 17 Nov 2024   Prob (F-statistic):            0.00169\n",
      "Time:                        17:29:24   Log-Likelihood:                -131.67\n",
      "No. Observations:                 246   AIC:                             277.3\n",
      "Df Residuals:                     239   BIC:                             301.9\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===========================================================================================================================================\n",
      "                                                                              coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------------------------------------------------------------\n",
      "Intercept                                                                   1.0517      0.329      3.195      0.002       0.403       1.700\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Copilot]              0.2159      0.067      3.222      0.001       0.084       0.348\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Human Creativity]     0.1957      0.067      2.938      0.004       0.064       0.327\n",
      "DAT                                                                        -0.0019      0.004     -0.489      0.626      -0.009       0.006\n",
      "Experience                                                                  0.0866      0.044      1.977      0.049       0.000       0.173\n",
      "Ability                                                                    -0.1284      0.046     -2.785      0.006      -0.219      -0.038\n",
      "English                                                                    -0.0668      0.065     -1.029      0.304      -0.195       0.061\n",
      "==============================================================================\n",
      "Omnibus:                       36.863   Durbin-Watson:                   2.127\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               45.121\n",
      "Skew:                          -1.014   Prob(JB):                     1.59e-10\n",
      "Kurtosis:                       2.465   Cond. No.                     1.02e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.02e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('Again ~ C(Group, Treatment(reference=\"Human Confirmation\")) + DAT + Experience + Ability + English',\n",
    "                data=tmp[tmp.Day==2]).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06e90937",
   "metadata": {},
   "source": [
    "# Table S.12: Satisfaction with AI Assistance Across Groups on Day 2 (Writing with AI)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "fc3346b4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:         AI_Helpfulness   R-squared:                       0.039\n",
      "Model:                            OLS   Adj. R-squared:                  0.015\n",
      "Method:                 Least Squares   F-statistic:                     1.634\n",
      "Date:                Sun, 17 Nov 2024   Prob (F-statistic):              0.138\n",
      "Time:                        17:32:47   Log-Likelihood:                -430.67\n",
      "No. Observations:                 246   AIC:                             875.3\n",
      "Df Residuals:                     239   BIC:                             899.9\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===========================================================================================================================================\n",
      "                                                                              coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------------------------------------------------------------\n",
      "Intercept                                                                   5.9662      1.110      5.374      0.000       3.779       8.153\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Copilot]              0.5087      0.226      2.252      0.025       0.064       0.954\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Human Creativity]     0.4987      0.225      2.220      0.027       0.056       0.941\n",
      "DAT                                                                        -0.0024      0.013     -0.186      0.853      -0.028       0.023\n",
      "Experience                                                                  0.2134      0.148      1.444      0.150      -0.078       0.504\n",
      "Ability                                                                    -0.1537      0.155     -0.989      0.324      -0.460       0.152\n",
      "English                                                                    -0.2543      0.219     -1.161      0.247      -0.686       0.177\n",
      "==============================================================================\n",
      "Omnibus:                       33.838   Durbin-Watson:                   2.014\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               43.556\n",
      "Skew:                          -1.008   Prob(JB):                     3.48e-10\n",
      "Kurtosis:                       3.426   Cond. No.                     1.02e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.02e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "tmp = df.groupby(by=['ID', 'Day'])[['Group', 'AI_Helpfulness', 'AI_Satisfaction', 'AI_Contribution', \n",
    "                                    'DAT', 'Ability', 'Experience', 'English']].first().reset_index()\n",
    "model = smf.ols('AI_Helpfulness ~ C(Group, Treatment(reference=\"Human Confirmation\")) + DAT + Experience + Ability + English',\n",
    "                data=tmp[tmp.Day==2]).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "66aa596c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:        AI_Satisfaction   R-squared:                       0.097\n",
      "Model:                            OLS   Adj. R-squared:                  0.074\n",
      "Method:                 Least Squares   F-statistic:                     4.280\n",
      "Date:                Sun, 17 Nov 2024   Prob (F-statistic):           0.000406\n",
      "Time:                        17:33:43   Log-Likelihood:                -458.46\n",
      "No. Observations:                 246   AIC:                             930.9\n",
      "Df Residuals:                     239   BIC:                             955.4\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===========================================================================================================================================\n",
      "                                                                              coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------------------------------------------------------------\n",
      "Intercept                                                                   5.5564      1.243      4.471      0.000       3.108       8.005\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Copilot]              1.0134      0.253      4.008      0.000       0.515       1.512\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Human Creativity]     0.7336      0.251      2.918      0.004       0.238       1.229\n",
      "DAT                                                                         0.0023      0.014      0.160      0.873      -0.026       0.031\n",
      "Experience                                                                  0.3120      0.165      1.886      0.061      -0.014       0.638\n",
      "Ability                                                                    -0.4830      0.174     -2.776      0.006      -0.826      -0.140\n",
      "English                                                                    -0.2617      0.245     -1.067      0.287      -0.745       0.221\n",
      "==============================================================================\n",
      "Omnibus:                       18.684   Durbin-Watson:                   1.906\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               21.493\n",
      "Skew:                          -0.723   Prob(JB):                     2.15e-05\n",
      "Kurtosis:                       2.921   Cond. No.                     1.02e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.02e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('AI_Satisfaction ~ C(Group, Treatment(reference=\"Human Confirmation\")) + DAT + Experience + Ability + English',\n",
    "                data=tmp[tmp.Day==2]).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "99bda8f8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:        AI_Contribution   R-squared:                       0.262\n",
      "Model:                            OLS   Adj. R-squared:                  0.243\n",
      "Method:                 Least Squares   F-statistic:                     14.13\n",
      "Date:                Sun, 17 Nov 2024   Prob (F-statistic):           9.17e-14\n",
      "Time:                        17:34:48   Log-Likelihood:                -1010.1\n",
      "No. Observations:                 246   AIC:                             2034.\n",
      "Df Residuals:                     239   BIC:                             2059.\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===========================================================================================================================================\n",
      "                                                                              coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------------------------------------------------------------\n",
      "Intercept                                                                 106.4512     11.704      9.096      0.000      83.396     129.507\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Copilot]            -13.5237      2.381     -5.679      0.000     -18.215      -8.833\n",
      "C(Group, Treatment(reference=\"Human Confirmation\"))[T.Human Creativity]   -20.5582      2.368     -8.683      0.000     -25.222     -15.894\n",
      "DAT                                                                        -0.2659      0.136     -1.956      0.052      -0.534       0.002\n",
      "Experience                                                                  1.8735      1.558      1.203      0.230      -1.195       4.942\n",
      "Ability                                                                    -2.5069      1.638     -1.530      0.127      -5.734       0.720\n",
      "English                                                                     1.8897      2.309      0.819      0.414      -2.658       6.438\n",
      "==============================================================================\n",
      "Omnibus:                       33.183   Durbin-Watson:                   2.113\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               42.698\n",
      "Skew:                          -0.925   Prob(JB):                     5.35e-10\n",
      "Kurtosis:                       3.863   Cond. No.                     1.02e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.02e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('AI_Contribution ~ C(Group, Treatment(reference=\"Human Confirmation\")) + DAT + Experience + Ability + English',\n",
    "                data=tmp[tmp.Day==2]).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fadb6998",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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